I picked up a KitchenAid bottom mount fridge back in December. Previous owner stated it worked fine for the first eight years they had it then it stopped cooling. They replaced the motherboard about a year and a half ago (less than a year before I got it). He said it worked fine for months and then stopped cooling again and out of frustration, it was time to get rid of it. It had sat unplugged for a couple of weeks before I got it. I got it home, plugged it in and it worked great!! For about three months. Then, it stopped cooling. After leaving it unplugged for a few days (and loosing my inventory), plug it in and it works great! For about three months. Then it stops cooling again. This cycle has happened three or four times in the eight months I've had it. What happens.... all lights work, all fans seem to work, you can hear a whine down by the condenser for about 3 seconds, it clicks and goes away for about 5 minutes and repeats <click, 3 second whine, click> and will keep repeating as long as it's plugged in. If I leave it unplugged overnight, plug it in and it cools until temperature is reached. Then it begins the cycle again. I've recently replaced the Start Dev (relay) and that had no effect.
Appreciate the help.

Will do. Further detail, I've taken my compressor nozzle and cleaned all grates, vents, tubing and fan blades. The fan does function, but perhaps not fast enough. The bulbous metal container (condenser?) is very hot to the touch. Near burning when my forearm brushed it.

You probably have a seizing compressor when it gets warm, amprobe would verify.

If the compressor will not start with the oem start device, the compressor is damaged, not repairable